Genomic selection (GS) can be effective in breeding for quantitative traits, such as yield, by reducing the selection cycle duration. Speed breeding (SB) uses extended photoperiod and temperature control to enable rapid generation advancement. Together, GS and SB can synergistically reduce the breeding cycle by quickly producing recombinant inbred lines (RILs) and enabling indirect phenotypic selection to improve for key traits, such as height and flowering time, prior to field trials. In addition, traits measured under SB (SB traits) correlated with field‐based yield could improve yield prediction in multivariate GS. A 193‐line spring wheat (Triticum aestivum L.) training population (TP), tested for grain yield in the field in multiple environments, was used to predict grain yield of a 350‐line selection candidate (SC) population, across multiple environments. Four SB traits measured on the TP and SC populations were used to derive principal components, which were incorporated into multivariate GS models. Predictive ability was significantly increased by multivariate GS, in some cases being twice as high as univariate GS. Based on these results, an efficient breeding strategy is proposed combining SB and multivariate GS using yield‐correlated SB traits for yield prediction. The potential for early indirect SB phenotypic selection for targeted population improvement prior to trials was also investigated. Plant height and flowering time showed strong relative predicted efficiency to indirect selection, in some cases as high as direct field selection. The higher selection intensity and rate of generation turnover under SB may enable a greater rate of genetic gain than direct field phenotyping.